The study of fluctuations of the injected and dissipated power in
a system driven out of equilibrium by an external force is
nowadays a widely studied problem which is not yet completely
understood. This is a very important and general issue within the
context of Fluctuation Theorems (FT) which constitute extremely
useful relations for characterizing the probabilities of observing
entropy production or consumption in out of equilibrium systems.
These relations were first observed in the simulations of a
sheared fluid[1]} and later proved both for chaotic
dynamical systems [2]} and for stochastic
dynamics[3]}. These works lead to different
formulations which find powerful applications for measuring
free-energy difference in biology (see e.g. [4]} for a
review). The hypothesis and the extensions of fluctuation
theorems[5]}
have been tested in various
experimental systems such as colloidal
particles[6]}, [7]}, [8]}, mechanical
oscillators[9]}, electric circuits[10]} and optically driven
single two-level systems[11]}. The effect of
anharmonic potential on the motion of a colloidal particle has
been tested by Blickle et al
[6]}, [13]}, [11]}. In
a recent experiment [15]} it has been shown that FT holds for
a colloidal particle confined in a double well potential and
driven out of equilibrium near the stochastic resonance (see next
section). The purpose of this article is to compare the probability density function (PDF) for
work and heat measured in this experiment with those analytically
computed from a non-linear Langevin dynamics. We also discuss the
difference between the PDF obtained from a phase average of the
driving and those obtained from a fixed phase only. Such a precise
comparison between theory and experiment in a double well
potential driven out of equilibrium has never been done before.
There is only
a numerical study, which has explored the distributions
of the dissipated heat and of the work in a Langevin dynamics near
the stochastic resonance [16]}, [17]}. The paper is
organized as follow. The properties of the stochastic resonance
are recalled in the next section. The experimental set-up is
described in section 3. The analytical PDF are derived in
section 4. The comparison between the theoretical predictions and
the experimental measurements is done in section 5. Finally we
conclude in section 6.
